Interpreting Inequality Solutions - Pre Algebra

1. If $t$ is hours worked and $t \le 8$, what does the solution mean?

   At most 8 hours: any amount of time up to and including 8 hours.

2. Spending at most 30 dollars on items that cost 6 dollars each gives $n \le 5$. What does the solution mean?

   At most 5 items can be bought; any whole number from 0 to 5 works.

3. In words, what does the solution $p > 50$ mean?

   $p$ is more than 50; 50 itself is not included.

4. The solution $h < 4$ describes safe heights in meters. What does it say about a height of exactly 4 meters?

   4 meters is not safe. The strict symbol $<$ excludes 4.

5. The solution set is $x < -1$. Which value belongs to it: $-2$ or $0$?

   $-2$, since $-2 < -1$. The value 0 is greater than $-1$.

6. A problem about buses needed gives $b \ge 4.2$. What is the least number of buses?

   5. Buses come in whole numbers, and 4 buses is less than 4.2.

7. A model gives $w > -2$ for the width $w$ of a garden in meters. Which values make sense in context?

   Only $w > 0$. A width must be positive, so the context narrows the solution.

8. How many numbers satisfy an inequality such as $x > 3$?

   Infinitely many: every real number greater than 3, including non-integers like 3.5.

9. Which inequality symbol matches the phrase "at most"?

   $\le$. For example, $x \le 10$ means $x$ is no more than 10.

10. A problem about tickets gives $n \le 12.5$. What is the greatest number of tickets?

    12. Tickets come in whole numbers, so the largest whole number not above 12.5 is 12.

11. In words, what does the solution $x \ge -5$ mean?

    $x$ can be $-5$ or any number greater than $-5$.

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